Learning from the uncertain:
Modelling and forecasting of
infectious disease outbreaks


Sebastian Funk
12 December, 2017
Imperial College Bioinformatics

Metcalf & Lessler (Science, 2017)

Forecasting the Ebola epidemic

Summer 2014

\(y=ax+b\)

\begin{eqnarray} \dot{S}&=&-\beta \frac{S}{N}I\\ \dot{I}&=&+\beta \frac{S}{N}I - \gamma I\\ \dot{R}&=&+\gamma I \end{eqnarray}

\(y=ax+b\)

A semi-mechanistic model for real-time forecasting

The unknown

  • Community/hospital/funeral transmission
  • Spatial dynamics
  • Changes in behaviour
  • Changes in reporting
  • Interventions
  • Seasonality
  • etc

The known

  • Average incubation period (~9 days)
  • Average infectious period (~11 days)
  • Case-fatality rate (~70%)

WHO Ebola response team (NEJM, 2014)

Time-varying transmission rate with smoothing prior

\(d\log \beta_t = \sigma dW_t\)

Dureau et al. (Biostatistics, 2013)

Particle MCMC

Andrieu et al. (J R Stat Soc B, 2010), Dureau et al. (arXiv, 2013), Murray et al. (arXiv, 2013)

  • \(d\log \beta_t = \sigma dW_t\)
  • Negative binomial observations, overdispersion \(\phi\)
  • \(\theta=\{\sigma, \phi, \beta_0, I_0\}\)
    • Intensity of random walk
    • Overdispersion of reporting
    • Initial transmission rate
    • Initial number infective

Camacho et al. (PLoS Current, 2015), Funk et al. (Epidemics, 2016)

How good were the forecasts?

"Evaluate predictive performance on the basis of maximising the sharpness of the predictive distribution subject to calibration"

Gneiting et al. (J R Stat Soc B, 2007)

Calibration: Compatibility of forecasts and observations.

Funk et al. (bioRxiv, 2017)

Sharpness: Concentration of predictive distribution

Funk et al. (bioRxiv, 2017)

Learning from the uncertain

Filtered trajectories tell us something about dynamics

Example: Ebola outbreak in Lofa Country, Liberia

An attempt to tease out factors that controlled Ebola

Funk et al. (Phil Trans R Soc B, 2017)

An attempt to tease out factors that controlled Ebola

Funk et al. (Phil Trans R Soc B, 2017)

Example: age of infection in childhood infections

Outlook

Metcalf & Lessler (2017)

Forecasts are becoming part of outbreak response

Forecasting challenges

Challenges in real-time modelling and forecasting

Need methods to
combine all available data streams
(individual/behavioural/spatial/genetic)

Challenges in real-time modelling and forecasting

Louis du Plessis, University of Oxford (unpublished)

Computationally efficient tools

Computationally efficient tools

Computationally efficient tools

Quality of forecasts vs quality of decisions

Acknowledgements

Anton Camacho, John Edmunds, Roz Eggo,
Rachel Lowe, Adam Kucharski (LSHTM)
James Hensman (Lancaster), Lawrence Murray (Uppsala)

Thank you!

http://sbfnk.github.io